Measurement and Conversion

Multiple Choice Identify the letter of the choice that best completes the statement or answers the question.

Complete the following using metric measurements.

____ 1. A car is about ____ long. a. 4 km c. 4 cm b. 4 g d. 4 m

____ 2. A trout has a mass of about ____. a. 1 kg c. 1 km b. 1 g d. 1 mL

____ 3. A glass of water holds about ____. a. 200 km c. 200 m b. 200 L d. 200 mL

____ 4. A pizza is about ____ wide. a. 26 mL c. 26 cm b. 26 m d. 26 g

____ 5. A small pebble has a mass of about ____. a. 20 g c. 20 L b. 20 kg d. 20 mL

____ 6. A bottle of juice holds about ____. a. 2 m c. 2 L b. 2 mL d. 2 g

____ 7. Convert 3.44 mm to centimeters. a. 0.0344 cm c. 3.44 cm b. 34.4 cm d. 0.344 cm

____ 8. Convert 7.54 g to kilograms. a. 7.54 kg c. 0.754 kg b. 0.0000754 kg d. 0.00754 kg

____ 9. Convert 633 mL to liters. a. 0.00633 L c. 0.000633 L b. 6.33 L d. 0.633 L

____ 10. How many feet is 18 yards equal to? a. 54 feet c. 648 feet b. 54 yards d. 3 yards

____ 11. How many ounces is 8 pounds equal to? a. 16 ounces c. 128 ounces b. 192 ounces d. 16,000 ounces

____ 12. How many fluid ounces is 19 cups equal to? a. 38 fluid ounces c. 8 fluid ounces b. 152 fluid ounces d. 166 fluid ounces

____ 13. Find the perimeter of the figure. 41 cm 34 cm

a. 172 cm c. 75 cm b. 86 cm d. 109 cm

____ 14. Find the perimeter of the figure.

a. 60 ft c. 432 ft b. 42 ft d. 84 ft

____ 15. What is the perimeter of the polygon?

16 ft 24 ft

a. 132 ft c. 104 ft b. 76 ft d. 28 ft

____ 16. Find the area of the rectangle.

3 cm a. 18 cm 2 c. 36 cm 2 b. 18 cm 2 d. 9 cm 2

____ 17. Find the area of the triangle.

9 ft a. 16.5 ft2 c. 108 ft2 b. 54 ft2 d. 10.5 ft2

____ 18. Find the missing value of the circle below to the nearest hundredth. Use 3.14 for .

C = 25.12

a. d = 16.00 m c. d = 4.00 m b. d = 12.56 m d. d = 8.00 m

____ 19. Find the area of the circle below to the nearest hundredth. Use for .

a. A = 110 m2 c. A = 15,400 m2 b. A = 220 m2 d. A = 3,850 m2

____ 20. Convert 56 liters to centiliters. a. 560 liters c. 5,600 liters b. 0.56 liters d. 56,000 liters

____ 21. Find the perimeter of the polygon. 18 ft

20 ft 20 ft

a. 158 ft c. 7,560 ft b. 79 ft d. 60 ft

____ 22. Find the perimeter of the polygon.

16 in.

8 in. 8 in.

16 in.

a. 48 in. c. 128 in. b. 40 in. d. 24 in.

____ 23. Find the perimeter of the rectangle.

a. 96 cm c. 48 cm b. 512 cm d. 80 cm

____ 24. Find the circumference of the circle below to the nearest tenth. Use 3.14 for . 13 cm

a. 1666.3 cm c. 40.8 cm b. 81.6 cm d. 530.7 cm

____ 25. Find the area of the rectangle. 8.2 m

a. 155.8 m2 c. 27.2 m2 b. 311.6 m2 d. 54.4 m2

____ 26. Find the area of the triangle.

a. 26 square units c. 8.5 square units b. 72 square units d. 36 square units

____ 27. Find the area of the triangle. 7

a. 9 square units c. 29 square units b. 38.5 square units d. 77 square units

____ 28. Find the area of the circle to the nearest tenth. Use 3.14 for .

6.6 ft

a. 136.8 ft2 c. 429.5 ft2 b. 41.4 ft2 d. 547.1 ft2

____ 29. Find the area of the circle to the nearest tenth. Use 3.14 for .

3.2 cm

a. 32.2 cm2 c. 25.2 cm2 b. 10 cm2 d. 8 cm2

____ 30. Use the Pythagorean Theorem to find the missing measure. c 9 m

a. 21 m c. 225 m b. 15 m d. 7.94 m

____ 31. The baseball diamond at a playground is a square with sides that measure 75 feet. About how long would a straight line be from home plate to second base? Round your answer to the nearest tenth.

2nd base

Home plate

a. 75 feet c. 150 feet b. 11,250 feet d. 106.1 feet

Short Answer

32. A box of cereal weighs 450 grams. a. How many kilograms does it weigh? Show your work. b. How many milligrams does it weigh? Show your work. Measurement and Conversion Answer Section

MULTIPLE CHOICE

1. ANS: D Find the most appropriate unit of measure. 1 meter 3.28 feet 1 kilometer 0.62 mile

KEY: measurement, appropriate units NOT: /A/The best approximation is shorter than this. A kilometer is more than half a mile. /B/A gram is a measure of mass, not length. /C/The best approximation is longer than this. A centimeter is less than an inch long. /D/Correct!

2. ANS: A Find the most appropriate unit of measure. 1 gram the mass of a paper clip 1 kilogram 2.2 pounds

KEY: measurement, appropriate units NOT: /A/Correct! /B/The best approximation is greater than this. A paper clip has a mass of about 1 gram. /C/A kilometer measures length, not mass. /D/A milliliter measures volume, not mass.

3. ANS: D Find the most appropriate unit of measure. Milliliters and liters are the only units of capacity in the choices. 200 mL = 0.2 L Soft drinks are sold in 2-liter containers. So 200 L would be equivalent to 100 of these 2-liter containers. This would be much too large.

KEY: measurement, appropriate units NOT: /A/A kilometer measures length, not capacity. /B/The best approximation is less than this. 200 L is equivalent to 100 2-liter bottles. /C/A meter measures length, not capacity. /D/Correct!

4. ANS: C Find the most appropriate unit of measure. Centimeters and meters are the only units of length in the choices. 1 meter 3.28 feet 2.54 centimeters 1 inch

KEY: measurement, appropriate units NOT: /A/A millileter is a measure of capacity, not a measure of length. /B/The best approximation is shorter than this. A meter is more than 3 feet long. /C/Correct! /D/A gram is a measure of mass, not a measure of length.

5. ANS: A Find the most appropriate unit of measure. Grams and kilograms are the only units of weight in the choices. 1 kilogram 2.2 pounds 28 grams 1 ounce

KEY: measurement, appropriate units NOT: /A/Correct! /B/The best approximation is smaller than this. 20 kg is about 44 pounds. /C/A liter measures volume, not mass. /D/A milliliter measures volume, not mass.

6. ANS: C Find the most appropriate unit of measure. Liters and milliliters are the only units of capacity in the choices. 1 milliliter the capacity of an eye dropper Soft drinks are sold in 2 liter containers.

KEY: measurement, appropriate units NOT: /A/A meter measures length, not capacity. /B/The best approximation is larger than this. A thimble has a capacity of about 2 mL. /C/Correct! /D/A gram measures mass, not capacity. 7. ANS: D Place value chart: 1000 100 10 1 0.1 0.01 0.001 Thousands Hundreds Tens Ones Tenths Hundredths Thousandths Kilo- Hecto- Deca- Base unit Deci- Centi- Milli-

To convert from a larger unit to a smaller unit, multiply by the difference in the powers of ten between the units. To convert from a smaller unit to a larger unit, divide by the difference in the powers of ten between the units.

KEY: metric system, measurement, converting NOT: /A/Are your powers of ten correct?/B/Are you converting to the proper units? /C/Are you converting to the proper units? /D/Correct!

8. ANS: D Place value chart: 1000 100 10 1 0.1 0.01 0.001 Thousands Hundreds Tens Ones Tenths Hundredths Thousandths Kilo- Hecto- Deca- Base unit Deci- Centi- Milli-

KEY: metric system, measurement, converting NOT: /A/Are you converting to the proper units? /B/Are your powers of ten correct? /C/Are you converting to the proper units? /D/Correct!

9. ANS: D Place value chart: 1000 100 10 1 0.1 0.01 0.001 Thousands Hundreds Tens Ones Tenths Hundredths Thousandths Kilo- Hecto- Deca- Base unit Deci- Centi- Milli-

KEY: metric system, measurement, converting NOT: /A/Are your powers of ten correct? /B/Are you converting to the proper units? /C/Are you converting to the proper units? /D/Correct!

10. ANS: A Set up the proportion and cross multiply to solve for x. A sample proportion would be as follows:

KEY: proportion, measurement NOT: /A/Correct! /B/Which unit of measurement are you solving for? /C/Are you using the correct length conversion? /D/Did you set up a proportion containing the correct length conversion?

11. ANS: C Set up the proportion and cross multiply to solve for x. A sample proportion would be as follows:

KEY: proportion, measurement NOT: /A/Did you find the conversion for the correct numbers of units? /B/Did you set up a proportion using the weight conversion as one ratio? /C/Correct! /D/Are you using the correct weight conversion?

12. ANS: B Set up the proportion and cross multiply to solve for x. A sample proportion would be as follows:

KEY: proportion, measurement NOT: /A/Are you using the correct capacity conversion? /B/Correct! /C/This is the number in one unit. /D/Did you set up a proportion using the capacity conversion as one ratio?

13. ANS: B The perimeter of a figure is the sum of the lengths of its sides.

KEY: perimeter, polygon NOT: /A/ Did you multiply the sum by two? /B/ Correct! /C/ Is this the distance around the entire figure? /D/ How do you find the perimeter of a rectangle?

14. ANS: D The perimeter of a rectangle is the added measurements of all four sides. Multiply each side length by 2, in order to include both sides of the rectangle, and then add the two products together.

KEY: perimeter, formula NOT: /A/ Is this the distance around the entire rectangle?/B/ Did you remember to add the opposite side length of the rectangle? /C/ Is this the perimeter or area of the figure? /D/ Correct!

15. ANS: C The length of the unknown side is the sum of the two sides opposite the unknown side. The perimeter is the sum of all the lengths of the sides of the figure.

KEY: perimeter, polygon NOT: /A/ Should you add the unknown value to the perimeter twice?/B/ Is this the perimeter of the entire figure or just the combined lengths of the known sides? /C/ Correct! /D/ Is this the perimeter of the figure or the length of the unknown side?

16. ANS: B The area of the rectangle is its length times its width.

KEY: area, rectangle NOT: /A/ Is this the perimeter of the rectangle or the area of the rectangle? /B/ Correct! /C/ Did you multiply the area by 2?/D/ Is the area of a rectangle its length times its width or its length plus its width?

17. ANS: B

To find the area of the triangle, multiply by the base of the triangle by the height of the

triangle.

KEY: area, triangle NOT: /A/ Is the area of a triangle 1/2 times the base plus the height? /B/ Correct! /C/ Did you remember to multiply by 1/2? /D/ Should you add the height and the base before you multiply by 1/2?

18. ANS: D The formula for the circumference of a circle is 2 times the radius times , or if the diameter is given, the formula for the circumference is the diameter times .

KEY: circle, circumference, formula NOT: /A/ Did you use the formula for area or circumference? /B/ Did you square pi?/C/ Are you using the radius or the diameter in the formula for the circumference? /D/ Correct!

19. ANS: D The formula for the area of a circle is A = r2.

KEY: circle, area, formula NOT: /A/ Did you remember to square the radius of the circle? /B/ Is this the area of the circle or the circumference of the circle? /C/ Should you use the radius or diameter of the circle to find the area?/D/ Correct! 20. ANS: C To convert from kilounits to units, multiply by 1000. To convert from units to centiunits, multiply by 100. To convert from units to milliunits, multiply by 1000. To convert from milliunits to units, divide by 1000. To convert from centiunits to units, divide by 100. To convert from units to kilounits, divide by 1000.

KEY: convert, metric NOT: /A/Did you place a decimal correctly? /B/Is your answer a reasonable estimate? /C/Correct! /D/Check your conversion.

21. ANS: B The perimeter of a polygon is the distance around the figure. So to determine the perimeter, the student should determine the sum of the side lengths.

KEY: perimeter, polygon NOT: /A/Did you use too many steps to solve the problem? /B/Correct! /C/Did you use the correct operations to find the perimeter? /D/How do you determine the perimeter?

22. ANS: A To find the perimeter of the polygon, add the lengths of the four sides.

KEY: perimeter, polygon NOT: /A/Correct! /B/Did you remember all four sides?/C/Did you use the correct operations to find perimeter? /D/How do you determine the perimeter of a polygon?

23. ANS: A To find the perimeter of a rectangle the student must add the measurements of all four sides together. So in this example the student will need to multiply each side length by two, in order to include both sides of the rectangle, and then add the two products together.

KEY: perimeter, rectangle NOT: /A/Correct! /B/This is the area of the rectangle. /C/Did you remember the opposite sides of the rectangle? /D/Did you remember to account for all four sides of the rectangle?

24. ANS: B To find the circumference of a circle, multiply 2 by the radius by pi, or if the diameter is given, multiply the diameter by pi.

KEY: circle, circumference NOT: /A/Check the formula for finding the circumference. /B/Correct! /C/Are you using the radius or the diameter to determine the circumference? /D/This is the area of the circle.

25. ANS: A To find the area of the rectangle, multiply the length by the width.

KEY: area, rectangle NOT: /A/Correct! /B/Check the formula used for finding the area of a rectangle. /C/Check the formula used for finding the area of a rectangle. /D/This is the perimeter of the rectangle.

26. ANS: D

To find the area of the triangle, multiply the base of the triangle by the height of the triangle.

KEY: area, triangle NOT: /A/The area of a triangle is half the area of a parallelogram with the same base and height. /B/The area of a triangle is half the area of a parallelogram with the same base and height. /C/The area of a triangle is half the area of a parallelogram with the same base and height. /D/Correct!

27. ANS: B To find the area of the right triangle, multiply the length of one leg by the length of the other leg and divide by 2. The legs are the base and height of a right triangle since they meet at a right angle.

KEY: area, triangle NOT: /A/The area of a triangle is half the product of the height and the base. /B/Correct! /C/The area of a triangle is half the product of the height and the base. /D/The area of a triangle is half the product of the height and the base.

28. ANS: A To find the area of a circle, multiply  by the square of the circle’s radius.

KEY: area, circle NOT: /A/Correct! /B/This is the circumference of the circle. /C/Remember to apply order of operations. /D/Did you use the square of the radius or the square of the diameter?

29. ANS: D To find the area of a circle, multiply  by the square of the circle’s radius. If you know the diameter, divide by 2 to find the radius.

KEY: area, circle NOT: /A/Does the formula for area use the radius or the diameter? /B/This is the circumference of the circle. /C/Remember to apply the order of operations. /D/Correct!

30. ANS: B The Pythagorean Theorem is a2 + b2 = c2, where c is the length of the hypotenuse. If you are solving for either a or b, then solve the theorem for that variable: c2 – b2 = a2 or c2 – a2 = b2.

KEY: Pythagorean Theorem, right triangle NOT: /A/Check the Pythagorean Theorem./B/Correct! /C/Did you remember to take the square root to get your final answer? /D/Which side of the triangle are you solving for?

31. ANS: D Since the baseball diamond is a square, the distance between home plate and second base is the hypotenuse of a triangle. So we can use the Pythagorean Theorem — a2 + b2 = c2, where the length from second to home is c, to solve this problem.

KEY: Pythagorean Theorem, right triangle NOT: /A/Check the Pythagorean Theorem. /B/Did you remember to take the square root of your answer? /C/Check the Pythagorean Theorem. /D/Correct!

SHORT ANSWER

32. ANS: a. 0.45 kg

b. 450,000 mg

KEY: measurement, metric measurement, decimal